fix(terminal): the Path and Clear keys act on the tile or Pane B that has the keyboard

The phone keyboard's Path key (insertTerminalText) and its clear-prompt key
(clearTerminalInput) always wrote to the main pane: into its local-echo
overlay, or to the active session. With the tile grid open that overlay is
parked behind the grid, so a picked path landed there unseen and only reached
the session later, and with the split open a path meant for Pane B went to
Pane A.

Both now ask _focusedPane() first. When a tile or Pane B holds the keyboard,
the path is sent to that pane's session through the exactly-once queue, and
clearing sends Ctrl+U there (those panes have no overlay, so the TUI owns the
line), then the pane's own terminal takes focus. The main pane's behaviour is
unchanged. Left over from the final checkup's dictation fix (c10), which
covered voice input only.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

test/path-picker-ui.test.ts

@@ -225,6 +225,60 @@ describe('mobile filesystem picker actions', () => {
     expect(terminalHarness.cjkClear).toHaveBeenCalled();
   });
 
+  it('sends a picked path to the tile or Pane B that holds the keyboard, never the parked main overlay', () => {
+    const appendText = vi.fn();
+    const sendInput = vi.fn();
+    const _sendInputAsync = vi.fn();
+    const mainFocus = vi.fn();
+    const tileFocus = vi.fn();
+    const app = {
+      activeSessionId: 'session-1',
+      _localEchoEnabled: true,
+      _localEchoOverlay: { appendText },
+      terminal: { focus: mainFocus },
+      sendInput,
+      _sendInputAsync,
+      _focusedPane: () => ({ terminal: { focus: tileFocus }, sessionId: 'tile-2', isPrimary: false, tile: {} }),
+    };
+
+    terminalHarness.mixin.insertTerminalText.call(app, '/mnt/d/AI/project');
+
+    expect(_sendInputAsync).toHaveBeenCalledWith('tile-2', '/mnt/d/AI/project');
+    expect(appendText).not.toHaveBeenCalled();
+    expect(sendInput).not.toHaveBeenCalled();
+    expect(tileFocus).toHaveBeenCalledOnce();
+    expect(mainFocus).not.toHaveBeenCalled();
+  });
+
+  it('clears the prompt of the tile or Pane B that holds the keyboard with Ctrl+U, leaving the main overlay alone', () => {
+    const clear = vi.fn();
+    const sendInput = vi.fn(() => Promise.resolve());
+    const _sendInputAsync = vi.fn();
+    const showToast = vi.fn();
+    const tileFocus = vi.fn();
+    const app = {
+      activeSessionId: 'session-1',
+      _inputFlushTimeout: null,
+      _pendingInput: 'main pane text',
+      _localEchoEnabled: true,
+      _localEchoOverlay: { getFlushed: () => ({ count: 0, text: '' }), clear, suppressBufferDetection: vi.fn() },
+      sendInput,
+      _sendInputAsync,
+      showToast,
+      terminal: { focus: vi.fn() },
+      _focusedPane: () => ({ terminal: { focus: tileFocus }, sessionId: 'tile-2', isPrimary: false, tile: {} }),
+    };
+
+    terminalHarness.mixin.clearTerminalInput.call(app);
+
+    expect(_sendInputAsync).toHaveBeenCalledWith('tile-2', '\x15');
+    expect(sendInput).not.toHaveBeenCalled();
+    expect(clear).not.toHaveBeenCalled();
+    expect(app._pendingInput).toBe('main pane text');
+    expect(showToast).toHaveBeenCalledWith('Input cleared', 'success');
+    expect(tileFocus).toHaveBeenCalledOnce();
+  });
+
   it('uses Ctrl+U to clear the TUI-owned prompt when local echo is disabled', () => {
     const sendInput = vi.fn(() => Promise.resolve());
     const app = {